#include "perm.h"
#include<iostream>
#include<vector>
#include<deque>
using namespace std;
#define int long long
vector<int32_t> construct_permutation(int k)
{
int k1 = k;
int k2 = 1;
for(int i = min(k-1,(int) 1e5); i >= 1; i--) {
if(k%i == 0) {
k1 = i;
k2 = k/i;
break;
}
}
vector<int32_t> vc;
deque<int> ans;
int lg = 0;
for(int i = 0; i <= 60; i++) {
if(k1 >= (1LL<<i)) lg = i;
}
for(int i = lg-1; i >= 0; i--) {
ans.push_back((int) ans.size());
if(k1&(1LL<<i)) ans.push_front((int) ans.size());
}
// cout << " " << k1 << endl;
for(auto x : ans) {
// cout << " 1 " << x << endl;
vc.push_back(x);
}
deque<int> ans2;
int lg2 = 0;
for(int i = 0; i <= 60; i++) {
if(k2 >= (1LL<<i)) lg2 = i;
}
for(int i = lg2-1; i >= 0; i--) {
ans2.push_back((int) ans2.size()+vc.size());
if(k2&(1LL<<i)) ans2.push_front((int) ans2.size()+vc.size());
}
// cout << " " << k2 << endl;
for(auto x : ans2) {
// cout << " 2 " << x << endl;
vc.push_back(x);
}
return vc;
}
